This paper presents an approach to defining distances between nonlinear and hybrid dynamical systems based on formal power series theory. The main idea is that the input-output behavior of a wide range of dynamical systems can be encoded by rational formal power series. Hence, a natural distance between dynamical systems is the distance between the formal power series encoding their input-outpu...

In this paper, a specific neural-based model for identification of dynamical nonlinear systems is proposed. This artificial neural network, called State-Space Neural Network (SSNN), is different from other existing neural networks. Indeed, it uses a state-space representation while being able to adapt and learn its parameters. These parameters are the neural weights which are intelligible or un...

It is shown how functional-analytic gradient-holonomic structures can be used for an isospectral integrability analysis of nonlinear dynamical systems on discrete manifolds. The approach developed is applied to obtain detailed proofs of the integrability of the discrete nonlinear Schrödinger, Ragnisco–Tu and Riemann–Burgers dynamical systems.

We study parallel solution methods for time-dependent problems where the domain decomposition is in the time variable. We show that Newton’s method can be used to create parallelism in nonlinear dynamical systems. We demonstrate that arbitrarily large speedups can be expected for sufficiently small time steps. Thus we conclude that nonlinear dynamical systems do not form essentially sequential ...

This paper deals with a normal form of a class of nonlinear dynamical systems. This form enables us to design a reduced-order observer for a class of nonlinear dynamical system. Necessary and sufficient geometrical conditions for the existence of a coordinate change to transform a given singular dynamical system into such normal form are also given.

The sensitive dependence of periodicity and chaos on parameters is investigated for three-dimensional nonlinear dynamical systems. Previous works have found that noninvertible low-dimensional maps present power-law exponents relating the uncertainty between periodicity and chaos to the precision on the system parameters. Furthermore, the values obtained for these exponents have been conjectured...

This paper discusses memory neuron networks as models for identification and adaptive control of nonlinear dynamical systems. These are a class of recurrent networks obtained by adding trainable temporal elements to feedforward networks that makes the output history-sensitive. By virtue of this capability, these networks can identify dynamical systems without having to be explicitly fed with pa...

A conservation law and stability, recovering phenomena and characteristic patterns of a nonlinear dynamical system have been studied and applied to biological and ecological systems. In our previous study, we proposed a system of symmetric 2n-dimensional conserved nonlinear differential equations with external perturbations. In this paper, competitive systems described by 2-dimensional nonlinea...

This paper conducts a stability, robustness and sensitivity analysis on a pointwise-optimal control law developed for dynamical systems. Many dynamical systems are described by complex nonlinear equations, which makes it difficult to design controllers for them. Pointwise-optimal control emerges as a viable design for such systems. We quantify the sources of errors for dynamical systems and pro...